|
# |
ODE |
Program classification |
CAS classification |
Solved? |
Verified? |
time (sec) |
|
\[ {}\left (2 x -y+2\right ) y^{\prime }+3+6 x -3 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.756 |
|
|
\[ {}\left (3+2 x -y\right ) y^{\prime }+2 = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
0.776 |
|
|
\[ {}\left (4+2 x -y\right ) y^{\prime }+5+x -2 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.676 |
|
|
\[ {}\left (5-2 x -y\right ) y^{\prime }+4-x -2 y = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.998 |
|
|
\[ {}\left (1-3 x +y\right ) y^{\prime } = 2 x -2 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.745 |
|
|
\[ {}\left (2-3 x +y\right ) y^{\prime }+5-2 x -3 y = 0 \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.981 |
|
|
\[ {}\left (4 x -y\right ) y^{\prime }+2 x -5 y = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.383 |
|
|
\[ {}\left (6-4 x -y\right ) y^{\prime } = 2 x -y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.574 |
|
|
\[ {}\left (1+5 x -y\right ) y^{\prime }+5+x -5 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.514 |
|
|
\[ {}\left (a +b x +y\right ) y^{\prime }+a -b x -y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.61 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime }+x = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class C‘]] |
✓ |
✓ |
0.72 |
|
|
\[ {}\left (x^{2}-y\right ) y^{\prime } = 4 x y \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.272 |
|
|
\[ {}\left (y-\cot \left (x \right ) \csc \left (x \right )\right ) y^{\prime }+\csc \left (x \right ) \left (1+y \cos \left (x \right )\right ) y = 0 \] |
exactWithIntegrationFactor |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
41.14 |
|
|
\[ {}2 y y^{\prime }+2 x +x^{2}+y^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
1.248 |
|
|
\[ {}2 y y^{\prime } = x y^{2}+x^{3} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.678 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime } = y \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.911 |
|
|
\[ {}\left (2 y+x \right ) y^{\prime }+2 x -y = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
exact, differentialType, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.19 |
|
|
\[ {}\left (1+x -2 y\right ) y^{\prime } = 1+2 x -y \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.033 |
|
|
\[ {}\left (1+x +2 y\right ) y^{\prime }+1-x -2 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.711 |
|
|
\[ {}\left (1+x +2 y\right ) y^{\prime }+7+x -4 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.697 |
|
|
\[ {}2 \left (x +y\right ) y^{\prime }+x^{2}+2 y = 0 \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.186 |
|
|
\[ {}\left (3+2 x -2 y\right ) y^{\prime } = 1+6 x -2 y \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.346 |
|
|
\[ {}\left (1-4 x -2 y\right ) y^{\prime }+2 x +y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.0 |
|
|
\[ {}\left (6 x -2 y\right ) y^{\prime } = 2+3 x -y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.848 |
|
|
\[ {}\left (19+9 x +2 y\right ) y^{\prime }+18-2 x -6 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.625 |
|
|
\[ {}\left (x^{3}+2 y\right ) y^{\prime } = 3 x \left (2-x y\right ) \] |
exact, differentialType |
[_exact, _rational, [_1st_order, ‘_with_symmetry_[F(x),G(x)]‘], [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.348 |
|
|
\[ {}\left (\tan \left (x \right ) \sec \left (x \right )-2 y\right ) y^{\prime }+\sec \left (x \right ) \left (1+2 y \sin \left (x \right )\right ) = 0 \] |
unknown |
[[_Abel, ‘2nd type‘, ‘class A‘]] |
❇ |
N/A |
6.388 |
|
|
\[ {}\left (x \,{\mathrm e}^{-x}-2 y\right ) y^{\prime } = 2 x \,{\mathrm e}^{-2 x}-\left ({\mathrm e}^{-x}+x \,{\mathrm e}^{-x}-2 y\right ) y \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.798 |
|
|
\[ {}3 y y^{\prime }+5 \cot \left (x \right ) \cot \left (y\right ) \cos \left (y\right )^{2} = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
5.5 |
|
|
\[ {}3 \left (2-y\right ) y^{\prime }+x y = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.803 |
|
|
\[ {}\left (x -3 y\right ) y^{\prime }+4+3 x -y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.618 |
|
|
\[ {}\left (4-x -3 y\right ) y^{\prime }+3-x -3 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.747 |
|
|
\[ {}\left (2+2 x +3 y\right ) y^{\prime } = 1-2 x -3 y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.739 |
|
|
\[ {}\left (5-2 x -3 y\right ) y^{\prime }+1-2 x -3 y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.742 |
|
|
\[ {}\left (1+9 x -3 y\right ) y^{\prime }+2+3 x -y = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.846 |
|
|
\[ {}\left (x +4 y\right ) y^{\prime }+4 x -y = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.891 |
|
|
\[ {}\left (3+2 x +4 y\right ) y^{\prime } = 1+x +2 y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.718 |
|
|
\[ {}\left (5+2 x -4 y\right ) y^{\prime } = 3+x -2 y \] |
exact, differentialType, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.953 |
|
|
\[ {}\left (5+3 x -4 y\right ) y^{\prime } = 2+7 x -3 y \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.467 |
|
|
\[ {}4 \left (1-x -y\right ) y^{\prime }+2-x = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
1.184 |
|
|
\[ {}\left (11-11 x -4 y\right ) y^{\prime } = 62-8 x -25 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.689 |
|
|
\[ {}\left (6+3 x +5 y\right ) y^{\prime } = 2+x +7 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.254 |
|
|
\[ {}\left (7 x +5 y\right ) y^{\prime }+10 x +8 y = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.203 |
|
|
\[ {}\left (x +4 x^{3}+5 y\right ) y^{\prime }+7 x^{3}+3 x^{2} y+4 y = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✗ |
N/A |
1.106 |
|
|
\[ {}\left (5-x +6 y\right ) y^{\prime } = 3-x +4 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.732 |
|
|
\[ {}3 \left (2 y+x \right ) y^{\prime } = 1-x -2 y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
0.709 |
|
|
\[ {}\left (3-3 x +7 y\right ) y^{\prime }+7-7 x +3 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.565 |
|
|
\[ {}\left (1+x +9 y\right ) y^{\prime }+1+x +5 y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.249 |
|
|
\[ {}\left (8+5 x -12 y\right ) y^{\prime } = 3+2 x -5 y \] |
exact, differentialType, homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
3.115 |
|
|
\[ {}\left (140+7 x -16 y\right ) y^{\prime }+25+8 x +y = 0 \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.699 |
|
|
\[ {}\left (3+9 x +21 y\right ) y^{\prime } = 45+7 x -5 y \] |
homogeneousTypeMapleC, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class C‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.666 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+x = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class C‘], _dAlembert] |
✓ |
✓ |
17.747 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+y = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.525 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime }+b x +a y = 0 \] |
exact, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _exact, _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
1.478 |
|
|
\[ {}\left (x a +b y\right ) y^{\prime } = b x +a y \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class A‘]] |
✓ |
✓ |
2.796 |
|
|
\[ {}x y y^{\prime }+1+y^{2} = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.368 |
|
|
\[ {}x y y^{\prime } = x +y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.72 |
|
|
\[ {}x y y^{\prime }+x^{2}+y^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.955 |
|
|
\[ {}x y y^{\prime }+x^{4}-y^{2} = 0 \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _rational, _Bernoulli] |
✓ |
✓ |
0.75 |
|
|
\[ {}x y y^{\prime } = a \,x^{3} \cos \left (x \right )+y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class D‘], _Bernoulli] |
✓ |
✓ |
0.971 |
|
|
\[ {}x y y^{\prime } = x^{2}-x y+y^{2} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.839 |
|
|
\[ {}x y y^{\prime }+2 x^{2}-2 x y-y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.984 |
|
|
\[ {}x y y^{\prime } = a +b y^{2} \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.295 |
|
|
\[ {}x y y^{\prime } = a \,x^{n}+b y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
1.063 |
|
|
\[ {}x y y^{\prime } = \left (x^{2}+1\right ) \left (1-y^{2}\right ) \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
12.514 |
|
|
\[ {}x y y^{\prime }+x^{2} \operatorname {arccot}\left (\frac {y}{x}\right )-y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
2.49 |
|
|
\[ {}x y y^{\prime }+x^{2} {\mathrm e}^{-\frac {2 y}{x}}-y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
0.916 |
|
|
\[ {}\left (x y+1\right ) y^{\prime }+y^{2} = 0 \] |
exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.757 |
|
|
\[ {}x \left (y+1\right ) y^{\prime }-\left (1-x \right ) y = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.731 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1+x \right ) y = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.76 |
|
|
\[ {}x \left (1-y\right ) y^{\prime }+\left (1-x \right ) y = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.755 |
|
|
\[ {}x \left (y+2\right ) y^{\prime }+x a = 0 \] |
quadrature |
[_quadrature] |
✓ |
✓ |
0.319 |
|
|
\[ {}\left (2+3 x -x y\right ) y^{\prime }+y = 0 \] |
exactWithIntegrationFactor |
[_rational, [_1st_order, ‘_with_symmetry_[F(x)*G(y),0]‘], [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.839 |
|
|
\[ {}x \left (4+y\right ) y^{\prime } = 2 x +2 y+y^{2} \] |
first_order_ode_lie_symmetry_calculated |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.195 |
|
|
\[ {}x \left (y+a \right ) y^{\prime }+b x +c y = 0 \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.438 |
|
|
\[ {}x \left (y+a \right ) y^{\prime } = y \left (B x +A \right ) \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.269 |
|
|
\[ {}x \left (x +y\right ) y^{\prime }+y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.396 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+y^{2} = 0 \] |
exactByInspection, homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.925 |
|
|
\[ {}x \left (x +y\right ) y^{\prime } = x^{2}+y^{2} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
0.95 |
|
|
\[ {}x \left (x -y\right ) y^{\prime }+2 x^{2}+3 x y-y^{2} = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.451 |
|
|
\[ {}x \left (x +y\right ) y^{\prime }-y \left (x +y\right )+x \sqrt {x^{2}-y^{2}} = 0 \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _dAlembert] |
✓ |
✓ |
1.695 |
|
|
\[ {}\left (a +x \left (x +y\right )\right ) y^{\prime } = b \left (x +y\right ) y \] |
unknown |
[_rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
❇ |
N/A |
0.633 |
|
|
\[ {}x \left (y+2 x \right ) y^{\prime } = x^{2}+x y-y^{2} \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
3.181 |
|
|
\[ {}x \left (4 x -y\right ) y^{\prime }+4 x^{2}-6 x y-y^{2} = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
5.661 |
|
|
\[ {}x \left (x^{3}+y\right ) y^{\prime } = \left (x^{3}-y\right ) y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.257 |
|
|
\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = \left (2 x^{3}-y\right ) y \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.253 |
|
|
\[ {}x \left (2 x^{3}+y\right ) y^{\prime } = 6 y^{2} \] |
first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class G‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.349 |
|
|
\[ {}y \left (1-x \right ) y^{\prime }+x \left (1-y\right ) = 0 \] |
exact, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
0.775 |
|
|
\[ {}\left (x +a \right ) \left (x +b \right ) y^{\prime } = x y \] |
exact, linear, separable, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.069 |
|
|
\[ {}2 x y y^{\prime }+1-2 x^{3}-y^{2} = 0 \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.704 |
|
|
\[ {}2 x y y^{\prime }+a +y^{2} = 0 \] |
exact, bernoulli, separable, first_order_ode_lie_symmetry_lookup |
[_separable] |
✓ |
✓ |
1.216 |
|
|
\[ {}2 x y y^{\prime } = x a +y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class G‘], _rational, _Bernoulli] |
✓ |
✓ |
0.686 |
|
|
\[ {}2 x y y^{\prime }+x^{2}+y^{2} = 0 \] |
exact, bernoulli, homogeneousTypeD2, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _exact, _rational, _Bernoulli] |
✓ |
✓ |
1.293 |
|
|
\[ {}2 x y y^{\prime } = x^{2}+y^{2} \] |
bernoulli, homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[[_homogeneous, ‘class A‘], _rational, _Bernoulli] |
✓ |
✓ |
0.924 |
|
|
\[ {}2 x y y^{\prime } = 4 x^{2} \left (2 x +1\right )+y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.618 |
|
|
\[ {}2 x y y^{\prime }+x^{2} \left (a \,x^{3}+1\right ) = 6 y^{2} \] |
bernoulli, exactWithIntegrationFactor, first_order_ode_lie_symmetry_lookup |
[_rational, _Bernoulli] |
✓ |
✓ |
0.755 |
|
|
\[ {}\left (3-x +2 x y\right ) y^{\prime }+3 x^{2}-y+y^{2} = 0 \] |
exact |
[_exact, _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
1.229 |
|
|
\[ {}x \left (x -2 y\right ) y^{\prime }+y^{2} = 0 \] |
homogeneousTypeD2, exactWithIntegrationFactor, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.421 |
|
|
\[ {}x \left (2 y+x \right ) y^{\prime }+\left (2 x -y\right ) y = 0 \] |
homogeneousTypeD2, first_order_ode_lie_symmetry_calculated |
[[_homogeneous, ‘class A‘], _rational, [_Abel, ‘2nd type‘, ‘class B‘]] |
✓ |
✓ |
2.434 |
|
|
|
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